Non-invasive analysis of blood-brain barrier permeability based on wavelet and machine learning approaches
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EPJ manuscript No.
(will be inserted by the editor)
Non-invasive analysis of blood-brain barrier
permeability based on wavelet and machine
learning approaches
Nadezhda Semenova1,2a , Konstantin Segreev1 , Andrei Slepnev1 , Anastasia
Runnova1,3 , Maxim Zhuravlev1,3 , Inna Blokhina1 , Alexander Dubrovsky1 , Oxana
Semyachkina-Glushkovskaya1,4 , and Jürgen Kurths1,4,5
arXiv:2103.05693v1 [nlin.AO] 9 Mar 2021
1
Saratov State University, Astrakhanskaya str., 83, Saratov, 410012, Russia
2
Département d’Optique P. M. Duffieux, Institut FEMTO-ST, Université Bourgogne-Franche-
Comté CNRS UMR 6174, Besançon, France
3
State Medical University, B. Kazachaya str., 112, Saratov, 410012, Russia
4
Physics Department, Humboldt University, Newtonstrasse 15, 12489 Berlin, Germany
5
Potsdam Institute for Climate Impact Research, Telegrafenberg A31, 14473 Potsdam,
Germany
Abstract. The blood-brain barrier plays a decisive role in protecting
the brain from toxins and pathogens. The ability to analyze the BBB
opening (OBBB) is crucial for the treatment of many brain diseases,
but it is very difficult to noninvasively monitor OBBB. In this paper
we analyse the EEG series of healthy rats in free behaviour and after
music-induced OBBB. The research is performed using two completely
different methods based on wavelet analysis and machine learning ap-
proach. Both methods enable us to recognize OBBB and are in a good
agreement with each other. The comparative analysis was carried out
using F-measures and ROC-curves.
1 Introduction
The blood-brain barrier (BBB) is a highly selective barrier, which is formed by mi-
crovascular endothelial cells surrounded by pericytes and perivascular astroglia. It
controls the penetration of blood-borne agents into the brain or the release of metabo-
lites and ions from the brain tissue to blood [1–3]. Therefore, the BBB plays a vital
role in protecting the brain against pathogens and toxins. The BBB disruption is
associated with aging, dementia, multiple sclerosis, Alzheimer’s disease, stroke, brain
trauma, infection and tumors [4]. The permeability of BBB can be varied by neu-
roendocrine regulation and may play a protective role in injury and stroke [5–8].
The ability to analyze the BBB opening (OBBB) is crucial for the treatment of
brain diseases, and it is very difficult to noninvasively monitor OBBB [9, 10]. There-
fore, there is a strong need to create many save methods of the assessment of the BBB
permeability in clinical practice. There has been substantial progress over the past
few years [9, 10]. Magnetic resonance tomography (MRI) is an often used technique
a
e-mail: nadya.i.semenova@gmail.com2 Will be inserted by the editor
for the monitoring of OBBB [10]. However, MRI is bulky and cannot be used bedside.
The MRI requests the use of contrast agents, which can be even toxic [11, 12]. The
latter limits its continuous application and usage, especially in the case of children and
patients with kidney pathology [13, 14]. Therefore, the development of novel promis-
ing real-time, bedside, non-invasive, label-free, economically beneficial and readily
applicable methods is of highest actual importance, and solving this problem would
open a novel era in effective diagnosis and therapy of brain diseases that cause acute
and chronical OBBB.
In this paper we consider two different approaches for analysing the OBBB by
using electroencephalogram (EEG) time series of healthy rats. The first method is
based on the wavelet analysis of EEG signals. This approach is widely used in many
biomedical papers [15, 16], partially in epilepsy research [17, 18], and sleep staging
[19, 20], which confirms its applicability in these tasks. Nowadays, the wavelet analysis
is one of the main tools for processing data in real time and creating brain-computer
interface (BCI) devices [21–23].
The second method uses a machine learning approach to analyze such EEG sig-
nals. Recently, machine learning has been increasingly used in brain activity analysis
[24–27]. The application of machine learning to recognize features of brain activity
leads to the use of artificial neural networks (ANNs) of different types and topologies.
Basically, ANNs do not analyze the EEG signal in its pure form, but use some char-
acteristics based on the EEGs. For example, power spectral density [28], statistical
features [29], wavelet transform [30], combinations of energies of different frequency
bands [31] etc. Typically, deep neural networks (DNNs) are used for classification and
recognition tasks. As one of examples, the automatic scoring of sleeping stage was
recently provided by applying a convolutional neural network [32]. In this work we
use DNN with feedforward coupling.
Despite the fact that both methods are based on completely different types of
analysis, they show a good ability in recognizing the OBBB. BBB permeability can
be evaluated in real time, searching for the EEG signal features, which can be found
out by using both wavelet analysis and machine learning approaches.
2 Experiment design and data recording
The experiments were conducted on the same five adult male Wistar-Kyoto rats (250-
280 g) in awake state and during opened BBB (OBBB). All procedures and experi-
ments were done in accordance with the “Guide for the Care and Use of Laboratory
Animals” [33]. The experimental protocols were approved by the Local Bioethics
Commission of the Humboldt University and the Saratov State University. The ani-
mals were kept in a light/dark environment with the lights on from 8:00 to 20:00 and
fed ad libitum with standard rodent food and water. The ambient temperature and
humidity were maintained at 24.5 ± 0.5◦ C and 40%–60%, respectively.
Ten days before the experiments, an optical window, a polyethylene catheter, and
two epidural EEG electrodes for chronic recordings of electrocorticogram (ECoG) in
free behavior were implanted; after surgery, animals were housed individually. The
first EEG1-recording was recorded over an hour from 1 to 2 p.m. 10 days after the
electrode implantation operation.
The day after the baseline EEG1-recording, the rats were underwent to inter-
mittent music. The detailed description of the protocol of music-induced OBBB is
described in [34]. To produce the music (70-90-100 dB and 11-10000 Hz, Scorpions
“Still loving you”) we used loudspeaker (ranging of sound intensity 0-130 dB, fre-
quencies 63-15000 Hz; 100 V, Yerasov Music Corporation, Saint Petersburg, Russia).
The repetitive music exposure was performed using a sequence of: 60 sec – music onWill be inserted by the editor 3
and then 60 sec – music off during 2h. The sound level was measured directly in a
cage of animals using the sound level meter (Megeon 92130, Russia). During the 60
min music-off, we performed in vivo real time fluorescent microscopy of OBBB for
Evans Blue (EB) dye (i.v.), which we detected as bright fluorescence around the cere-
bral microvessels in awake behaving rats. When we observed the optical signs of EB
leakage, EEG recordings in rats were performed during 60 min (EEG2). The choice
of time of EEG recordings was related to our previous results discovering the window
of music-induced OBBB that is 60-180 min after sound exposure [34–36]. After EEG
recordings, the rats decapitated and their brains were collected for confirmation of
OBBB for ED using confocal microscopy. The EEG recordings were collected and
analyzed using wavelet and machine learning approaches.
A two-channels cortical EEG/one channel electromyogram (EMG) (Pinnacle Tech-
nology, Taiwan) were recorded as follows. The rats were implanted two silver elec-
trodes (tip diameter 2–3 µm) located at a depth of 150 µm in the coordinates (L: 2.5
mm and D: 2 mm) from Bregma on either side of the midline under inhalation anes-
thesia with 2% isoflurane at 1L/min N2 O/O2 – 70:30. The head plate was mounted
and small burr holes were drilled. Afterward, EEG wire leads were inserted into the
burr holes on one side of the midline between the skull and the underlying dura.
EEG leads were secured with dental acrylic. An EMG lead was inserted in the neck
muscle. Ibuprofen (15 mg/kg) for the relief of postoperative pain was provided in
their water supply for two to three days prior to surgery and for three or more days
post-surgery. The rats were allowed 10 days to recover from surgery prior to beginning
the experiment.
All EEG recordings were supplemented with synchronous videography, on the ba-
sis of which a neurophysiologist marked out the states of behavioral sleep and wake-
fulness of animals. Since the standard sleep staging rules for rats are not available
currently, we referred the visual scoring criteria from these studies [37, 38]. Wake-
fulness, NREM, and REM were visually scored in 10 s epochs. EEG activity was
measured and compared in rats in awake state, during sleep, and after OBBB on the
same rats. Wakefulness was defined as a desynchronized EEG with low amplitude
and high-frequency dynamics (>10%, 8-12 Hz) and relatively high-amplitude EMG.
NREM sleep was recognized as synchronized activity with high amplitude, which is
dominated by low-frequency delta waves (0–4 Hz) comprising >30% of EEG wave-
forms/epoch and a lower amplitude EMG. REM was identified by the presence of
theta waves (5–10 Hz) comprising >20% of EEG waveforms/epoch with a low EMG
amplitude.
Thus, for each of the animals the EEG signals were recorded before and after
music-induced OBBB – EEG1 and EEG2, respectively.
3 Recognition of OBBB using time-frequency analysis
Today, one of the generally accepted nonlinear methods for processing and detect-
ing of oscillatory activity in biomedical signals is continuous wavelet transforma-
tion (CWT) [39–41]. CWT is sufficiently resistant to abrupt changes in the frequency
composition of the analyzed experimental signals, which makes it possible to ade-
quately analyze rather short time intervals of highly nonstationary signals. The CWT
for an arbitrary signal x(t) in the general form is defined as follows:
+∞
Z
∗
W (s, t0 ) = x(t)ψs,t0
(t)dt, (1)
−∞4 Will be inserted by the editor
where ψs,t0 (t) is the basic complex function, s is the time scale defining the width of
the wavelet, the symbol “*” denotes complex conjugation. Note that the time scales
s of the CWT allow a transition to the classical frequencies f of the Fourier spec-
trum. Therefore, for convenience and simplicity of the interpretation of the results,
we consider the results in the traditional plane (f, t0 ).
The basic Morlet function ψs,t0 (t) is often used to analyze the activity of the
brain [42, 43]. By analogy with the Fourier power spectrum F (f ) for f -frequencies
we can estimate the instantaneous frequency distribution of the CWT-energy
E(f, t0 ) = |W (f, t0 )|2 . (2)
CWT allows to analyse an experimental EEG signal x(t) simultaneously in the
frequency and time domains. Moreover, the CWT excess property is well known,
which is used to search for the fine time-frequency structure of experimental time
series, which can be only poorly detected by conventional spectral methods [44–47].
In this paper to analyze the oscillatory structure of the EEG, we use the CWT
“skeleton” method [48–52], which is based on a simplification of the entire surface
(f ; t) of the experimental signal x(t) by estimation only the main part of oscillatory
activity. For each moment of time t0 , it is necessary to search for the maxima in the
instantaneous CWT spectrum E(f, t) (2):
∀f ∈ δfmax , E(fmax , t0 ) ≥ E(f, t0 ), (3)
where fmax = sc1 is the CWT skeleton, δfmax is a δ - region of the fmax frequency
component. The first skeleton f1 is the global maximum in the surface W (f, t0 ), i. e.
the value of the frequency in the signal spectrum, which correlates with the maximum
of the oscillational energy. Further, for each moment of time, we detect a local maxima
sc1 > sc2 > . . . > scj > . . . > scnp , where np is the amount of skeletons.
Further, we limit the consideration of the oscillatory structure in EEG signals to
the frequency band ∆f [1; 2, 5] Hz. The choice of this “slow” frequency interval is due
to the evidence in the literature on the presence of biomarkers in brain slow activity
reflecting the BBB permeability changes [27, 59]. Thus, at each time moment t0 we
estimate which skeleton’s number N0 falls into a certain frequency range ∆f . And
next we calculate the average number of N (t) skeletons falling into the band ∆f over
the time interval ∆t = 50 sec.
In Fig. 1(a) the results of estimating the number of N (t) skeletons for one ex-
perimental animal are presented. We observe that the number of patterns in the low
frequency range ∆f1 increases after a powerful auditory impact (EEG2). After eval-
uating the distribution of the number of patterns for records EEG1 and EEG2, their
mean values differ hN iEEG1 6= hN iEEG2 (see Fig. 1(b)). A similar situation is ob-
served in the slow oscillatory activity of the EEG for all experimental animals. Next,
we use the detectable value hN iEEG2 as the threshold value that characterizes the
moment of BBB permeability changes.
For each experimental animal, individual threshold values were obtained hN iEEG2 =
{0, 31863; 0, 45614; 0, 462575; 0, 485995; 0, 52011}. Thus, we estimated the EEG-
dynamics of the brain activity based on the N (t)-dynamic. Generally, the value of
dependence N (t) in EEG2-record exceeded the threshold hN iEEG2 throughout first
third of the recording. Next, this value N (t) irregularly reduced towards the end of the
EEG2-record, when, apparently, the influence of the sound impact was compensated
by the neurophysiological system, and the BBB-permeability returned to its usual
value. Based on this, we assumed that the excess of the N (t) patterns number of the
hN iEEG2 threshold value correlated with an increase in the BBB permeability. So,
when the corresponding threshold value N (t) ≥ hN iEEG2 is exceeded, we assumed
that the permeability of the BBB was increased.Will be inserted by the editor 5
N (a) N (b)
1.0 1.0
0.6 0.6
⟨N⟩EEG1
⟨N⟩EEG2
0.2 0.2
t, sec. 0 0.1 0.2 0.3 P(N)
0 500 1000 1500 2000 2500 3000 3500
Fig. 1. Results of evaluating the wavelet-based characteristics for animal # 3. Panel (a)
shows the time-dependence of the N average number of CWT-skeletons in the frequency
range ∆f1 [1; 2, 5] Hz. The red line is the calculation result for EEG1, the green line cor-
responds to the characteristic for EEG2. The panel (b) represents the probability distri-
butions of N skeletons. Red color shows the distribution for EEG1 (no influence on the
BBB-permeability), and green – for EEG2 (after auditory impact). The arrows indicate the
mean values for each distribution.
4 ANN based method
In order to estimate the permeability of the BBB, a deep neural network is used.
The neural network was trained using an open-source library in Python [53]. The
use of EEG signals in their pure form is a non-trivial task for the ANN, since it
requires a large number of neurons and layers. This dimension problem can be solved
by specially prepared statistical characteristics calculated from these EEGs. There
is a number of papers on sleep recognition, in which the EEG signals were not used
by ANN, but their averages, variations and deviations from the mean [28–31, 54].
In the same manner here we use a signal-to-noise ratio (SNR) as such a statistical
characteristic. It is the ratio between the mean of the signal µ(·) and its standard
deviation σ(·):
µ(x)
SN R(x) = . (4)
σ(x)
Each point of this characteristic is prepared for some averaging window. The window
size is fixed to 30 seconds. In order to make the SNR realization smoother, the calcu-
lations were performed with a slowly shifting time window with a 1-second step. This
leads to a new temporal determination of SNR with a time step of 1 sec, where each
point corresponds to the SNR value obtained from a thirty-second window of EEG
data. Figure 2 shows the EEG of one of the animals (panels a, c) and the calculated
SNR characteristics (panels b, d).
To get the training SNR examples, we used EEG signals before (EEG1) and after
(EEG2) artificially increased permeability of the BBB [55]. During the training, the
fragments of SNR for the rat after music stimulation were marked as the expected
response “1” (i.e. BBB is open), while fragments of rats before this stimulation cor-
responded to the response “0” (i.e. BBB is closed). Thus, the ANN response to an
unknown signal can be interpreted as a degree of the averaged “permeability” of BBB
over the considered period of time.
The input layer of our ANN consists of 90 neurons. Each time the network receives
a 90-second SNR realization as an input. A smaller number of input neurons leads
to slower training and a sharp jump into overtraining. A larger number leads to
inaccuracies in the temporal marking, since it gives the response delay of more than
1.5 minutes. Also a few DNN configurations with constant numbers of neurons in the
hidden layers 200, 500, 1000 have been considered. A network with a variable number
of neurons in hidden layers (500×200×500×200) has shown the optimal results during6 Will be inserted by the editor
Open BBB
(a) 400
EEG
-200
(b) 2.5
SNR
0.5
Closed BBB
(c) 400
EEG
-200
(d) 2.5
SNR
0.5
0 500 1000 1500 2000 2500 3000 3500
time, sec.
Fig. 2. Examples of EEG signals (a,c) for animal # 1 and corresponding SNR characteristics
(eq. 4) shown in panels (b,d).
2.5 2.5 2.5 2.5
responce "1"
1
(a) (b)
SNR
1.5 1.5 1.5 1.5
0.9
0.5 0.5 0.5 0.5
0 30 60 90 0 30 60 90 0 30 60 90 0 30 60 90 0.8
2.5 2.5 2.5 2.5
0.7
responce "0"
SNR
output 0.6
SNR
1.5 1.5 1.5 1.5
Accuracy
0.5
0.5 0.5 0.5 0.5
0 30 60 90 0 30 60 90 0 30 60 90 0 30 60 90 0.4
0.3
0.2
Number of 0.1 Training
neurons 90, 200, 500, 200, 500, 200, 1 Cross-validation
0
hidden layers 0 50 100 150 200 250
Epoch
Fig. 3. Schematic diagram of considered DNN (panel a) and the dynamics of accuracy
during training depending on the epoch number (panel b)
training and testing. The network scheme and the training process are shown in Fig. 3.
All the layers have the sigmoid activation function f (x) = 1/(1 − e−x ).
For each of the rats the ANN was trained on the data of the remaining rats. This
increased the number of training and testing implementations. Each EEG recording
was done using two channels. The SNR and ANN markup were prepared for both
signals separately. To increase accuracy, the network responses for both channels
were multiplied. Thus, if the network recognises the inputs from both channels are
recognized simultaneously as “1” (BBB is open), then the final answer is “1”. If one
channel leads to the answer “0” and the second one leads to the answer “1”, then
the final response is “0”. Since the network produces a real number from 0 to 1, the
multiplication of responses from two channels can lead to an increase in intermediate
values. To eliminate this, the threshold 0.5 has been introduced. Since then, the
answers y ≥ 0.5 are regarded as “1” (BBB is open), while responses y < 0.5 complies
with “0” (BBB is closed). Figure 4 shows a temporal evolution of ANN responses for
an animal with an artificially open barrier, whose signals were shown in Fig. 2(a,b).
The gray line represents the result of multiplying the signals from both channels, and
red pints show the final answer with the threshold 0.5.
The ANN found 32% of the data similar to the open barrier for implementations
after music-induced OBBB. In the case of free behaviour, this percentage was 24%.
These ratios are averaged over all considered animals. In order to exclude the pecu-Will be inserted by the editor 7
Combined ANN response
ANN method with threshold
1
Markup based on ANN method
0.8
0.6
0.4
0.2
0
0 500 1000 1500 2000 2500 3000 3500
time, s.
Fig. 4. Temporal evolution of ANN responses for animal # 1 after music-induced OBBB.
The multiplication of network responses for both EEG channels is shown in gray. Red points
correspond to the binary classification after introducing the threshold 0.5. Green areas show
time intervals in which both markings coincide: (1) based on ANN answers and (2) wavelet
method from Sect. 3.
liarities of the training, the networks have been trained 5 times for each animal with
an accuracy of at least 96% (approximately 250 epochs). Table 5 shows the percent-
age of fragments recognized as OBBB for one animal after 5 trainings. Afterward,
the general percentage of fragments, recognized as OBBB, has been averaged over
all animals and over all five trainings. Figure 5 shows examples of SNR obtained us-
ing fragments of EEG signals recognized as signals with open BBB (top panels) and
closed BBB (bottom panels).
5 Comparison of two independent methods of data processing
Figure 4 shows the intersection of both methods from Sect. 3 and 4 by green back-
ground color. We find that both methods are in a good agreement with each other. To
test this numerically, the so-called F-measure [56] is applied, which is often used for
statistical analysis of binary classification. It is the harmonic mean between precision
and recall. The precision is the number of correctly identified positive results divided
by the number of all positive results, including those not identified correctly, and the
recall is the number of correctly identified positive results divided by the number of
all samples that should have been identified as positive. For such an assessment, one
can choose one of the methods as true, for example, the wavelet method, and then
count the number of matches of both methods for the answer “yes” (true-positive,
TP), the number of matches for the answer “no” (true-negative, TN), as well as mis-
matches (false-positive, FP, and false-negative, FN). Based on this, the F-measure is
calculated as follows:
TP TP PR
P = ,R = ,F+ = 2 (5)
TP + FP TP + FN P +R
Thus, the F-measure F + is an evaluation of the correctness for the answers “yes”.
If we replace all letters “P” by “N” in Eq. (5), and vice versa, then this will be an
estimate of the correctness for the answer “no”, which we denote as F − . Table 5
shows the results of calculating the F-measure for five ANN trainings, as well as the
averaged characteristics. Thus, according to the calculations of the F-measure, we can
conclude that the intersection of 35 % in the answers that the barrier is open, and8 Will be inserted by the editor
responce "1" 2.5 2.5 2.5 2.5
SNR
1.5 1.5 1.5 1.5
0.5 0.5 0.5 0.5
0 30 60 90 0 30 60 90 0 30 60 90 0 30 60 90
2.5 2.5 2.5 2.5
responce "0"
SNR
1.5 1.5 1.5 1.5
0.5 0.5 0.5 0.5
0 30 60 90 0 30 60 90 0 30 60 90 0 30 60 90
Fig. 5. Examples of input SNR implementations on which the neural network exhibited a
similarity to OBBB (top panels) and closed barrier (bottom panels).
Training: Tr.1 Tr.2 Tr.3 Tr.4 Tr.5 Averaged
% of open barrier in realization with an open barrier 35 22 21 38 27 28.5
% of open barrier in realization with free behaviour 24 18 13 24 20 19.8
F-measure on responses “BBB is open”, F + 0.38 0.35 0.32 0.38 0.34 0.35
F-measure on responses “BBB is closed”, F − 0.73 0.77 0.79 0.72 0.75 0.75
Table 1. Percentage of fragments recognized as OBBB and not, and F-measures of animal
# 1 for five ANN trainings on fragments of the other animals.
75 % in the answers about the closed barrier. These values, averaged over all animals,
are 28 % and 70 %.
Another measure that allows one to assess the quality of the classification is the
receiver operating characteristic (ROC-curve). The ROC curve is created by plotting
the true positive rate (T P R = T PT+F P
N ) against the false positive rate (F P R =
FP
F P +T N ) at various threshold settings [57, 58]. The classifier is considered to be good
if the ROC-curve is above the diagonal (see Fig. 6). However, the degree of success
of the classifier is roughly estimated by how far this curve is above the diagonal, and,
accordingly, how large is the area below it. Figure 6 shows the ROC curves for different
threshold values in cases of artificially opened BBB (orange color) and free behaviour
(blue color), when the rat can either sleep or be awake. The markings obtained by
the method, described in Sect. 3, were used as a verification data. Both curves are
above the diagonal, which indicates the similarity of the methods. In addition, the
figure shows the results of calculating the F-measures for both implementations with
variation of the threshold parameter. The points corresponding to the 0.5 threshold
are highlighted by red. As follows from the graphs of F-measures, the threshold 0.5
is optimal for positive and negative answers. An increase in the threshold leads to
an increase in false positives, and a decrease leads to a loss of sensitivity when the
network says that the barrier is always closed.
6 Conclusions
This work is devoted to the investigation of sustained changes in brain activity after
music-induced OBBB. BBB permeability is analyzed using two different methods –
wavelet estimation of the oscillatory characteristics of the EEG and machine learning
using SNR characteristics. The wavelet analysis demonstrated an increase in the num-
ber of arising oscillations in the low-frequency region (1 – 2.5 Hz), which is universalWill be inserted by the editor 9
(a) 1 (b) 0.8
0.6
F + score
0.8 0.4
0.2
0.6 0
0 0.2 0.4 0.6 0.8 1
TPR
threshold
0.4 (c) 1
F - score
0.2 0.5
diagonal line
free behaviour
artificially opened BBB
0 0
0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1
FPR threshold
Fig. 6. Statistical comparison of both methods using ROC-curve (panel a), and F-scores
(eq. 5) for positive (b) and negative (c) responses.
for all animals. However, the threshold for the increase in oscillatory activity in these
frequencies is highly individual for each animal.
The second method is based on the search of special features of SNR realisation
which are common for animals with OBBB. The use of a machine learning approach
allows us to demonstrate a high level of universality of the revealed “portrait” of the
electrical activity of the brain after an artificial increase in the permeability of the
BBB.
Despite the fact that both methods are based on different characteristics, they
show a good overlap both for animals with artificially open BBB and for animals
in free behaviour without any influences. Quantification of the methods agreement
was based on ROC curves and F-measures of positive and negative responses. Both
methods recognized a non-zero probability of opening the barrier for animals with
normal behaviour. It is possible that this effect is related to the constancy of brain
activity patterns during the physiological state of sleep. A number of authors have
linked spontaneous changes in BBB permeability to certain stages of sleep, promoting
a repair and clearance of brain tissue [35, 36, 59].
In the future, we plan to increase of the experimental groups and to include
instrumental methods of optical control of the BBB permeability. The preliminary
analysis of brain activity during the sleeping state of the animals is of our interest.
Probably, some sleep stages would be accompanied with the brain activity, similar to
the results of music-induced OBBB.
7 Acknowledgements
This work has been supported by the RF Government Grant No. 075-15-2019-1885
in part of the biological interpretation. In the part of the development of numeric
method of data analysis this work has been supported by the Council for Grants
of the President of the Russian Federation for the State Support of Young Russian
Scientists (project no. MD-645.2020.9).10 Will be inserted by the editor
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